Generalized Quantum Loop Program

In the classical computation, loop program is a very important class of programming language, so it is necessary to study loop program under the quantum computation. Quantum loop program whose body is unitary operator has been studied in detail by Ying Mingsheng, so the definitions of quantum loop program and its termination (almost termination), and the computation function on quantum loop program are given. In addition, the necessary and sufficient condition of program termination (almost termination) is also proved. Thus the sensitivity problem of almost termination to noise is solved. If general loop program's body is unitary operator and quantum loop program's nest is considered, the outer quantum loop program's body should be quantum computation rather than unitary operator according to the calculation function on quantum loop program. Therefore, quantum loop program whose body is quantum operation is defined, it is called general quantum loop program (GQLoop) in this paper. Besides, it is examined that quantum loop program's nest whose body is unitary operator is a general quantum loop program. At last, the necessary and sufficient condition of GQLoop termination (almost termination) are given based on the above-mentioned definition.The structure of this paper are as follows:some preliminaries, including four basic assumptions of quantum mechanics, the definition of projective measurement and some necessary notations are introduced in the first chapter of this paper. The definition and properties of general quantum loop program are given based on the definition of quantum loop program, and it is examined that quantum loop program is one special general quantum loop program in the second chapter. In the third chapter, the necessary and sufficient conditions of GQLoop termination (almost termination) are introduced and proved in terms of the necessary and sufficient condition of quantum loop termination (almost termination). Finally, the basic contents of this paper are summarized and some problems about future research are proposed.